1. Field of the Invention
The present invention relates to a method wherein it is possible to distinguish between a process characterized by a time series that describes a white noise and a Markov process, and wherein it is also possible to distinguish between a chaotic process and a chaotic process with underlying noise.
2. Description of the Prior Art
Technical fields in which it is of interest to draw conclusions about the future behavior of a time series from a measured time series can be seen, for example, in various areas of medicine. The prediction of a future course of a time series usually occurs given the assumption that the time series exhibits non-linear correlations between the samples of the time series. For example, a specific area of application within medicine is cardiology. Specifically in the problem area of sudden cardiac death, it is critical to recognize the early warning signs of sudden cardiac death in order to initiate counter-measures against the occurrence of sudden cardiac death as early as possible.
It generally represents a considerable problem to classify a measured signal, particularly an electrical signal, and its samples, for example, in a purely chaotic process, a chaotic process with underlying noise, a process with white noise or a Markov process.
For example, document [1] discloses the determination of what is referred to as a Kolmogorov entropy. Further, this document discloses that a correlation function, that is explained in greater detail later, be formed.
It is known from documents [2], [3] to classify the time series into different types of time series on the basis of correlation integrals of the samples of the time series.
In these methods, however, the problem occurs that certain types of processes and, thus, types of time series cannot be discriminated. For example, it is not possible to distinguish with these methods between a process that is characterized by a time series that describes a white noise and a Markov process.
With this method, further, it also is not possible to distinguish between a chaotic process and a chaotic process with underlying noise.